Covariance messing around

knitr::opts_chunk$set(message = FALSE)
knitr::opts_chunk$set(warning = FALSE)

Invent some TPCs (purple is f(T), orange is g(T))

make up temperature time series

set.seed(101)
time <- seq_along(1:100)
temps <- data.frame(temperature = runif(100, min = 5, max = 33), time = time)

plot temps over time

temp_plot <- temps %>% 
    ggplot(aes(x = time, y = temperature)) + geom_line(size = 1) +
    ylab("Temperature (°C)") + xlab("Time (days)")

temp_plot

get trait values

f_time_series <- data.frame(time = time, ftrait = sapply(X = temps$temperature, FUN = f_curve), temperature = temps$temperature)
g_time_series <- data.frame(time = time, gtrait = sapply(X = temps$temperature, FUN = g_curve), temperature = temps$temperature)

plot traits over time

Calculate rolling covariances over the time series with different time slice durations (2, 5, 10, 20 days)

all_cov <- left_join(covariances2, covariances5) %>% 
    left_join(covariances10) %>% 
    left_join(covariances20) %>% 
    gather(key = slice, value = covariance, 2:5) %>% 
    mutate(slice = str_replace_all(slice, "[a-z, .]", "")) %>% 
    rename(time_slice = slice) %>% 
    mutate(time_slice = as.numeric(time_slice))

Joining, by = "time_point"
Joining, by = "time_point"
Joining, by = "time_point"

Plot all together

tpcs

Now, focusing on the 2 day time slice only, check that <R0(T)> = <f(T)g(T)> = <f(T)><g(T)> + Cov[f(T), g(T)]

Looks like this isn’t working as I expected! i.e. the blue and green lines below should be lining up…Hmmm….

Now, focusing on the 10 day time slice only, check that <R0(T)> = <f(T)g(T)> = <f(T)><g(T)> + Cov[f(T), g(T)]

Looks like this isn’t working as I expected! i.e. the blue and green lines below should be lining up…Hmmm….

Ok let’s try something simpler.